Help making a algorithm [duplicate]

First of all, you need to iterate over the integers 0 to N, where N is the number of values in your string (let's call this iteration variable i). For each i you will then generate all sets containing i out of N numbers in your input.

For example, i == 0 will generate {}, i == 1 will generate {1},{2},{3} etc.

Now let's suppose that the value of i is fixed; this will let us proceed to understand what to do for each of these iterations. Obviously we will need some kind of nested loop, since we will be generating multiple (in the general case) output values for each value of i (e.g. we 'll generate 3 sets when i == 1, as shown earlier).

This is called generating combinations of i items out of N, and there is plenty of documentation available. For example, see Algorithm to return all combinations of k elements from n.

For an alternative approach treat the question as a problem in binary. Your set has three elements, so you need three binary digits. Each member of the set can either be present (1) or absent (0) in the result. Hence you can map the required results onto three digit binary numbers:

000 -> {}
001 -> {3}
010 -> {2}
011 -> {2, 3}
100 -> {1}
101 -> {1, 3}
110 -> {1, 2}
111 -> {1, 2, 3}

It is not difficult to generate the numbers from 0 (000) to 7 (111) and to extract the required combinations from them.